A slope-based decoupling algorithm to simultaneously control dual deformable mirrors in a woofer–tweeter adaptive optics system

Abstract

We propose a slope-based decoupling algorithm to simultaneously control the dual deformable mirrors (DMs) in a woofer-tweeter adaptive optics system. This algorithm can directly use the woofer's response matrix measured from a Shack-Hartmann wave-front sensor to construct a slope-based orthogonal basis, and then selectively distribute the largeamplitude low-order aberration to woofer DM and the remaining aberration to tweeter DM through the slope-based orthogonal basis. At the same moment, in order to avoid the two DMs generating opposite compensation, a constraint matrix used to reset tweeter control vector is convenient to be calculated with the slope-based orthogonal basis. Numeral simulation demonstrates that this algorithm has a good performance to control the adaptive optics system with dual DMs simultaneously. Compared with the typical decoupling algorithm, this algorithm can take full use of the compensation ability of woofer DM and release the stroke of tweeter DM to compensate high-order aberration. More importantly, it does not need to measure the accurate shape of tweeter's influence function and keeps better performance of restraining the coupling error with the continuous-dynamic aberration.

Learning Approach for Flexible Spherical/Aspherical Reflective Surface Control

“…2. (24) The actuating signal of each actuator was in the range [−1, 1] (with −1 and 1 as two extreme actuating voltages) and directly proportional to the actuator stroke. The centers of the actuators on the outer ring were situated 2.1 mm from the outer edge of the mirror surface.…”

“…(7) In recent research, various applications of DMs for changing the focus and for correction in imaging fields have also been proposed. (8) In these previous studies, methods of controlling the DM based on the influence matrix (IM) (9,10) or the electromechanical coupling model (11)(12)(13) were well established. Because the actuator positional error and electromechanical model error influence the control precision of DMs, which are ultimately manifested as the difference between the ideal surface (initial design) and the actual surface (as applied), these methods still face several difficulties, such as online stable measurement/compensation and a complicated iterative computation process to observe the IM solution; therefore, there is a limited field of view in which the electromechanical coupling effect can be applied.…”

Eigenmode Wavefront Decoupling Algorithm for LC–DM Adaptive Optics Systems

“…The distribution and decoupling methods of aberrations must be studied to prevent the correction loss caused by the opposite aberrations of each corrector, and the AO correction can be rendered unstable [15]. To achieve simultaneous working of dual correctors, researchers have proposed many decoupling control methods, including the two-step [16], Zernike limited term [17], control signal reset [18], Fourier mode [19], Lagrangian damped least square [20], and the wavelet mode decoupling [21] method. According to the results of reference [22], only two-step, Zernike limited term, and control signal reset methods are effective to suppress coupling aberrations.…”

Sparse sampling algorithm for deformable mirror control

“…Researchers have conducted extensive studies to efficiently and accurately control the surface shape of DMs [10][11][12][13][14][15][16][17]. The commonly used control methods can be divided into open-loop control and closed-loop control.…”

“…A DM closed-loop correction system based on the feedback data from the measuring wavefront is advantageous [11,12]. Traditional control methods include the matrix pseudo-inverse method, steepest descent (SD) method, and iterative learning control (ILC).…”